Find the value of the exponent of the given product. Write your answer as a reduced fraction or integer \( x^{\frac{3}{7}} \cdot x^{4}= \)

To simplify the expression \( x^{\frac{3}{7}} \cdot x^{4} \), you can use the **product of powers property** of exponents, which states that when you multiply two expressions with the same base, you add their exponents: \[ x^{a} \cdot x^{b} = x^{a+b} \] Applying this property: \[ x^{\frac{3}{7}} \cdot x^{4} = x^{\frac{3}{7} + 4} \] To add the exponents, it's helpful to express the integer \( 4 \) as a fraction with the same denominator as \( \frac{3}{7} \): \[ 4 = \frac{28}{7} \] Now, add the two fractions: \[ \frac{3}{7} + \frac{28}{7} = \frac{31}{7} \] So, the simplified expression is: \[ x^{\frac{31}{7}} \] **Answer:** \(\dfrac{31}{7}\)